Final Answer:
The result of sin^-1(0.8) - tan^-1(-1/4) is 67.17 degrees. This entails finding the angle with a sine value of 0.8 and subtracting the angle with a tangent value of -1/4.
Step-by-step explanation:
The task at hand involves computing the value of sin^-1(0.8) - tan^-1(-1/4). This necessitates employing trigonometric identities and inverse trigonometric functions. Beginning with sin^-1(0.8), we recognize this as the angle whose sine value is 0.8. Thus, sin^-1(0.8) equals 53.13 degrees. Simultaneously, tan^-1(-1/4) corresponds to the angle with a tangent value of -1/4, resulting in tan^-1(-1/4) being -14.04 degrees.
Subtracting these angles, we arrive at the final result: sin^-1(0.8) - tan^-1(-1/4) = 53.13 - (-14.04) = 67.17 degrees. Therefore, the expression evaluates to 67.17 degrees, denoting the measured angular difference. In summary, the meticulous application of trigonometric functions and their inverses elucidates the step-by-step derivation of the solution, culminating in the determination that sin^-1(0.8) - tan^-1(-1/4) equals 67.17 degrees.